[Back]

 (Selected)

A new definition of fractional derivative
Zhibao Zheng, Wei Zhao, Hongzhe Dai

Fractional symmetrical perturbation method of finding adiabatic invariants of disturbed dynamical systems
Ming-Jing Yang, Shao-Kai Luo

A variable order fractional constitutive model of the viscoelastic behavior of polymers
Ruifan Meng, Deshun Yin, Corina S. Drapaca

Fractional conformal invariance method for finding conserved quantities of dynamical systems
Shao-Kai Luo, Yun Dai, Xiao-Tian Zhang, Ming-Jing Yang

Nonlinear vibration of fractional viscoelastic plate: Primary, subharmonic, and superharmonic response
M. R. Permoon, H. Haddadpour, M. Javadi

Alternate stability switches induced by time delay in nonlinear fractional oscillators
Q. X. Liu, J. K. Liu, Y. M. Chen

Noether’s theorem of Hamiltonian systems with generalized fractional derivative operators
Hong-Bin Zhang, Hai-Bo Chen

Hidden extreme multistability in a novel 4D fractional-order chaotic system
Xu Zhang, Zhijun Li

The conservation laws with Lie symmetry analysis for time fractional integrable coupled KdV–mKdV system
S. Sahoo, S. Saha Ray

Chaos in a novel fractional order system without a linear term
Sen Zhang, Yicheng Zeng, Zhijun Li

Fractional Birkhoffian method for equilibrium stability of dynamical systems
Shao-Kai Luo, Jin-Man He, Yan-Li Xu

On the appearance of fractional operators in non-linear stress–strain relation of metals
F. P. Pinnola, G. Zavarise, A. Del Prete, R. Franchi

Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with fractional-order derivative term
Conrad Bertrand Tabi

Stochastic averaging of quasi integrable and non-resonant Hamiltonian systems excited by fractional Gaussian noise With Hurst index H ∈ (1/2,1)
M. L. Deng, Q. F. Lü, W. Q. Zhu

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers
Rui Xiao, HongGuang Sun, Wen Chen

A new fractional order hyperchaotic Rabinovich system and its dynamical behaviors
Jin-Man He, Fang-Qi Chen

Nonlocal-in-time kinetic energy in nonconservative fractional systems, disordered dynamics, jerk and snap and oscillatory motions in the rotating fluid tube
Rami Ahmad El-Nabulsi

Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems
Chuan-Jing Song, Yi Zhang

[Back]

https://www.sciencedirect.com/science/article/pii/S002216941930784X?via=ihub

Bed-load transport along widely graded river-beds typically exhibits anomalous dynamics, whose efficient characterization may require parsimonious stochastic models with pre-defined statistics involving the waiting time and hop distance distributions for sediment particles. This study employs a continuous time random walk (CTRW) model to characterize bed-load particle motions on a widely graded gravel-bed with cluster microforms built in our lab. Flume experiments guide the selection of the Mittag-Leffler (M-L) function as the waiting time distribution function, and the Lévy -stable density for the hop distance distribution function in the CTRW model. Monte Carlo simulations show that the resulting CTRW model can well capture the observed flume experimental data (with either a continuous or an instantaneous source) with coexisting super- and sub-dispersion behaviors in the bed-load transport process. Analyses further discover the dual impact of clusters on the dynamics of fine sediment particles. Some particles are more likely to be blocked or trapped by clusters, while others have a high probability to be accelerated by the flow accelerating belt between the clusters. Therefore, with proper statistical distributions and relevant parameters for sediment waiting times and hop distances, the CTRW model may efficiently capture the complex dynamics in sediment transport.

　

The present paper considers a delayed generalized fractional-order prey-predator model with interspecific competition. The existence of the nontrivial positive equilibrium is discussed, and some sufficient conditions for global asymptotic stability of the equilibrium are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delay as the bifurcation parameter. Finally, some numerical simulations are carried out to support the analytical results.